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Express the given expression without logs, in simplest form. Assume all variables represent positive values. (e^(ln(8sqrtw))) Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values.\newline(eln⁡(8w)) \left(e^{\ln (8 \sqrt{w})}\right) \newlineAnswer:

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Q. Express the given expression without logs, in simplest form. Assume all variables represent positive values.\newline(eln⁡(8w)) \left(e^{\ln (8 \sqrt{w})}\right) \newlineAnswer:
  1. Recognize Inverse Functions: We start by recognizing that the natural logarithm function ln⁡(x)\ln(x) is the inverse of the exponential function exe^x. Therefore, when we have eln⁡(x)e^{\ln(x)}, the two functions cancel each other out, and we are left with just xx. This is because eln⁡(x)=xe^{\ln(x)} = x for all x > 0.
  2. Apply Inverse Property: Apply the inverse property to the given expression eln⁡(8w)e^{\ln(8\sqrt{w})}. Since ee and ln⁡\ln are inverse functions, eln⁡(8w)e^{\ln(8\sqrt{w})} simplifies to 8w8\sqrt{w}.
  3. Simplify Expression: Now we have the simplified expression 8w8\sqrt{w}, which is already in its simplest form. There is no further simplification needed.

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